The propagation of EM radiation past wavelength-sized inhomogeneities is not well understood, yet is of importance for both microwave heating and diagnostic applications in tokamaks. The work presented in this thesis improves this understanding; for this purpose, EMIT-3D, a new finite-difference time-domain (FDTD) code implementing a cold-plasma model has been written to extend full-wave simulations of propagation in magnetized plasmas to 3D. The numerical development of the algorithm is presented and supported with a new stability analysis. Studies of propagation past density filaments (`blobs') are presented and compared with 2D simulations. The synergistic effects of blob density and width on scattering angle are investigated, resulting in the conclusion that even filaments of densities below beam critical density can cause significant deviation in beam paths over a wide frequency range. Further to this, the case of oblique incidence is an explicitly 3D interaction, and its effects have been calculated. The broadening and defocusing effect on microwave beams caused by realistic edge turbulence, observed in all magnetic fusion devices, is also investigated. A fluid model for edge turbulence is used to produce realistic turbulent profiles, which in turn are used to initialise a set of microwave propagation simulations. The effect of propagation through a turbulent layer is observed even at low fluctuation amplitude, and observed to have a peak when eddy sizes approach beam wavelength. This work supports MAST experiments using the SAMI diagnostic to image microwave emission from the plasma edge due to mode conversion from electron Bernstein waves; however, it has relevance for numerous microwave diagnostic, heating and current drive applications in plasmas.